On the root mean square quantitative chirality and quantitative symmetry measures - Université Paris Cité Accéder directement au contenu
Article Dans Une Revue Journal of Mathematical Physics Année : 1999

On the root mean square quantitative chirality and quantitative symmetry measures

Résumé

The properties of the root mean square chiral index of a d-dimensional set of n points, previously investigated for planar sets, are examined for spatial sets. The properties of the root mean squares direct symmetry index, defined as the normalized minimized sum of the n squared distances between the vertices of the d-set and the permuted d-set, are compared to the properties of the chiral index. Some most dissymetric figures are analytically computed. They differ from the most chiral figures, but the most dissymetric 3-tuples and the most chiral 3-tuples have a common remarkable geometric property: the squared lengths of the sides are each equal to three times a squared distance vertex to the mean point.
Fichier principal
Vignette du fichier
PMP.JMP_1999.pdf (78.02 Ko) Télécharger le fichier
Origine : Fichiers éditeurs autorisés sur une archive ouverte
Loading...

Dates et versions

hal-02122820 , version 1 (07-05-2019)

Licence

Copyright (Tous droits réservés)

Identifiants

Citer

Michel Petitjean. On the root mean square quantitative chirality and quantitative symmetry measures. Journal of Mathematical Physics, 1999, 40 (9), pp.4587-4595. ⟨10.1063/1.532988⟩. ⟨hal-02122820⟩
67 Consultations
690 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More